Internal problem ID [7998]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 522.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 50
dsolve(18*x^2*(1+x)*diff(y(x),x$2)+3*x*(5+11*x+x^2)*diff(y(x),x)-(1-2*x-5*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x}{6}} \left (\frac {x +1}{x}\right )^{\frac {1}{6}}+c_{2} {\mathrm e}^{-\frac {x}{6}} \left (\frac {x +1}{x}\right )^{\frac {1}{6}} \left (\int \frac {{\mathrm e}^{\frac {x}{6}}}{\left (x +1\right )^{\frac {7}{6}} \sqrt {x}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.555 (sec). Leaf size: 73
DSolve[18*x^2*(1+x)*y''[x]+3*x*(5+11*x+x^2)*y'[x]-(1-2*x-5*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x/6} \left (c_2 \int _1^x\frac {e^{\frac {K[1]}{6}} \sqrt [3]{\frac {K[1]}{K[1]+1}}}{K[1]^{5/6} (K[1]+1)^{5/6}}dK[1]+c_1\right )}{\sqrt [6]{\frac {x}{x+1}}} \]